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In a geometric sequence {an}, if a1 = 4 and r = 0.2, the first 4 terms in the sequence are...
A) {4, .8, .16, .032,...}.
B) {4, 20, 100, 500,...}.
C) {4, 4.2, 4.4, 4.6,...}.
D) {4, 3.8, 3.6, 3.4,...}.

Respuesta :

fatiimaovo
A.) {4,.8,.16,.032,...}


Begin with 4 and multiply by 0.2, the ratio, to obtain successive term.
ardni313

The first 4 terms in the sequence are...

A) {4, .8, .16, .032,...}.

Further explanation

Geometry sequence are series of numbers that have a constant ratio

or can be interpreted:

Each number is obtained by multiplying the previous number by a constant

The sequence can be:

a, ar, ar², ar³, ... etc.

Can be formulated

[tex]\large{\boxed{\bold x_n=ar^{n-1}}}[/tex]

where:

a is the first term, and

r is the common ratio

In an geometric sequence , if a1 = 4 and r = 0.2, the first 4 terms in the sequence are

  • n=1

[tex]\displaystyle x_1=4=a[/tex]

  • n=2

[tex]\displaystyle x_2=4\times 0.2^{2-1}\\\\x_2=4\times 0.2^{1}\\\\x_2=4\times 0.2\\\\x_2=0.8[/tex]

  • n=3

[tex]\displaystyle x_3=4\times 0.2^{3-1}\\\\x_2=4\times 0.2^{2}\\\\x_2=4\times 0.04\\\\x_2=0.16[/tex]

  • n=4

[tex]\displaystyle x_4=4\times 0.2^{4-1}\\\\x_2=4\times 0.2^{3}\\\\x_2=4\times 0.008\\\\x_2=0.032[/tex]

Learn more

a geometric sequence

https://brainly.com/question/1480821

Determine whether the sequence below is a geometric

https://brainly.com/question/978528

the formula for a finite geometric series

https://brainly.com/question/4520322

Keywords : a geometric sequence, the first term, the common ratio

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